Equations of hyperelliptic Shimura curves
We describe an algorithm that computes explicit models of hyperelliptic Shimura curves attached to an indefinite quaternion algebra over Q and Atkin-Lehner quotients of them. It exploits Cerednik-Drinfeld's nonarchimedean uniformisation of Shimura curves, a formula of Gross and Zagier for the endomo...
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| Format: | Article |
| Publication date: | 2010 |
| Country: | España |
| Institution: | Universitat Autònoma de Barcelona |
| Repository: | Dipòsit Digital de Documents de la UAB |
| Language: | English |
| OAI Identifier: | oai:ddd.uab.cat:60941 |
| Online Access: | https://ddd.uab.cat/record/60941 |
| Access Level: | Open access |
| Keyword: | Corbes el·líptiques Equacions |
| Summary: | We describe an algorithm that computes explicit models of hyperelliptic Shimura curves attached to an indefinite quaternion algebra over Q and Atkin-Lehner quotients of them. It exploits Cerednik-Drinfeld's nonarchimedean uniformisation of Shimura curves, a formula of Gross and Zagier for the endomorphism ring of Heegner points over Artinian rings and the connection between Ribet's bimodules and the specialization of Heegner points, as introduced in [21]. As an application, we provide a list of equations of Shimura curves and quotients of them obtained by our algorithm that had been conjectured by Kurihara. |
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